An Equation for the Prediction of Human Skin Permeability of Neutral Molecules, Ions and Ionic Species

An Equation for the Prediction of Human Skin

Permeability of Neutral Molecules, Ions and Ionic Species

Item Type

Article

Authors

Zhang, K.; Abraham, M.H.; Liu, Xiangli

Citation

Zhang K, Abraham MH and Liu X (2017) An equation for the

prediction of human skin permeability of neutral molecules, ions

and ionic species. International Journal of Pharmaceutics. 521(1–

2): 259–266.

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Citation: Zhang K, Abraham MH and Liu X (2017) An equation for the prediction of human skin permeability of neutral molecules, ions and ionic species. International Journal of Pharmaceutics. 521(1–2): 259–266.

Accepted Manuscript

Title: An Equation for the Prediction of Human Skin

Permeability of Neutral Molecules, Ions and Ionic Species

Authors: Keda Zhang, Michael H. Abraham, Xiangli Liu

PII:

S0378-5173(17)30158-8

DOI:

http://dx.doi.org/doi:10.1016/j.ijpharm.2017.02.059

Reference:

IJP 16463

To appear in:

International Journal of Pharmaceutics

Received date:

17-1-2017

Revised date:

19-2-2017

Accepted date:

20-2-2017

Please cite this article as: Zhang, Keda, Abraham, Michael H., Liu, Xiangli,

An Equation for the Prediction of Human Skin Permeability of Neutral

Molecules, Ions and Ionic Species.International Journal of Pharmaceutics

http://dx.doi.org/10.1016/j.ijpharm.2017.02.059

1

An Equation for the Prediction of Human Skin Permeability of

Neutral Molecules, Ions and Ionic Species

Keda Zhang

_{, Michael H. Abraham}

_{, Xiangli Liu}

1

_{Department of Pharmacy, Wuhan Third Hospital, Wuhan 430060, China}

2

_{Central Laboratory of Longhua Branch, Shenzhen People’s Hospital, Second Clinical}

Medical College, Jinan University, Shenzhen 518109, China

3

_{Department of Chemistry, University College London, London WC1H 0AJ, UK}

4

_{Bradford School of Pharmacy, Faculty of Life Sciences, University of Bradford, Bradford}

BD7 1DP, UK

*

_{Corresponding author}

2

ABSTRACT

Experimental values of permeability coefficients, as log K

, of chemical compounds across

human skin were collected by carefully screening the literature, and adjusted to 37 ℃ for the

effect of temperature. The values of log K

for partially ionized acids and bases were separated

into those for their neutral and ionic species, forming a total data set of 247 compounds and

species (including 35 ionic species). The obtained log K

values have been regressed against

Abraham solute descriptors to yield a correlation equation with R

_{= 0.866 and SD = 0.432 log}

units. The equation can provide valid predictions for log K

of neutral molecules, ions and

ionic species, with predictive R

_{= 0.858 and predictive SD = 0.445 log units calculated by the}

leave-one-out statistics. The predicted log K

values for Na

and Et

N

are in good agreement

with the observed values. We calculated the values of log K

of ketoprofen as a function of

the pH of the donor solution, and found that log K

markedly varies only when ketoprofen is

largely ionized. This explains why models that neglect ionization of permeants still yield

reasonable statistical results. The effect of skin thickness on log K

was investigated by

4

INTRODUCTION

Rapid and accurate prediction of human skin permeability of chemical compounds is very

useful for developing dermal and transdermal drug delivery systems and cosmetics, as well

as evaluating environmental risks due to contact with skin.

Various kinds of empirical and

mathematical models for the correlation and prediction of human skin permeability, as log

K

, have been reported (Baba et al., 2015; Mitragotri, 2003), and there have been a number

of reviews of these models (Chen et al., 2013; Geinoz et al., 2004; Mitragotri et al., 2011; Moss

et al., 2011; Neely et al., 2009). It has been known for years that the permeability of ionizable

compounds depends on the pH of the donor solution, attributed to the slower rate of

permeation of ionic species compared to the corresponding neutral species (Roy and Flynn,

1990; Swarbrick et al., 1984; Waters and Bhuiyan, 2016). For instance, Waters and Bhuiyan

(2016) recently reported that as an in vitro skin mimic, silicone membrane encouraged

permeation of the more unionized forms of pharmaceutical compounds rather than the

ionized forms. However, the above reviews completely ignore the possibility of ionization and

associated factors such as the dependence of permeation on pH for ionizable compounds,

and our previous study represents the only attempt to include ionized species in a model for

skin permeation (Zhang et al., 2012). Thus one of the most popular models for skin

permeation, the Potts and Guy model (Potts and Guy, 1992), uses only the octanol-water

partition coefficient (as log P

) and molecular weight (MW) as compound descriptors (see

Eq. 1), with no reference to ionic species.

p o / w

log K



0.71log P

- 0.0061MW - 6.3

5

(LFER) model (Zhang et al., 2012). Since then, descriptors for considerably more compounds

have been obtained, including those for ionic species (Abraham and Acree, 2016), and it is the

purpose of the present work to set out an extended equation for the correlation and

prediction of human skin permeability, including neutral molecules and ionic species in the

same equation.

METHODS

LFER model

Our method is based on the LFER method of Abraham,

firstly

applied to the properties of

neutral molecules (Abraham, 1993) and subsequently extended to include ions and ionic

species by Abraham and Acree (Abraham, 2011; Abraham and Acree, 2010a, b, 2016)

.

The

general equation developed by Abraham and Acree is stated as:

SP = c + eE + sS + aA + bB + vV + j

_J

_{+ j}

_J

₍₂₎

The dependent variable SP represents an equilibrium coefficient for a series of solutes in a

given system, including partition coefficients (as log P) and rate coefficients (as log K), and in

the present work permeation coefficients through human skin, as log K

. The independent

variables are the physicochemical properties or descriptors of the solutes as follows. E is the

excess molar refraction in units of (cm

_{/mol)/10, S is the combined dipolarity/polarizability, A}

and B are the overall solute hydrogen bond acidity and basicity, and V is McGowan’s

characteristic molecular volume in units of (cm

_{/mol)/100; J}

_{and J}

_{are the additional}

descriptors that are specific to ionic species. Note that J

= 0 for anions, J

= 0 for cations, and

both J

and J

= 0 for neutral molecules. In the latter case, Eq. 2 reduces to an equation for

neutral molecules. We use the term “ions” for permanent ions such as Na

_{and Cl}

_{, and the}

6

of acidic compounds. The compound descriptors for neutral molecules are obtained from a

variety of experimental processes, as explained in a number of reviews (Abraham et al., 2004;

Clarke and Mallon, 2012; Poole et al., 2013), and Abraham and Acree have reviewed the

methods used to obtain descriptors for ions and ionic species (Abraham and Acree, 2016). The

coefficients (c, e, s, a, b, v, j

and j

) in Eq. 2 can be obtained by a multiple linear regression of

values of SP in a given system against the known solute descriptors, and used to characterize

the system of interest.

Effect of Temperature and Ionization

The reliability of the predictive model greatly depends upon the quality of the used database.

In this study, we ensured that measurements for the selected K

data were rigorously

conducted through in vitro passive diffusion study across excised human skin. As regards the

influence of temperature, we corrected values of log K

at various temperatures to obtain the

corresponding value at 37 ℃ as detailed by Abraham and Martins (2004) (see Table 1). The

determination of these corrections was quite coarse and also they should theoretically vary

with lipophilicity, but since they are comparatively small little error will be involved in just

using the corrections in Table 1.

Table 1. Corrections to log Kp from experimental temperature to 37

Adjusted temperatures Corrections to log Kp

from 20 to 37 0.69

from 25 to 37 0.48

from 30 to 37 0.28

from 32 to 37 0.20

7

The effect of ionization on skin permeation of compounds must be taken into

consideration, K

for neutral forms being much larger than that for ionic forms (Zhang et al.,

2012). Thus the fractions of neutral and ionic forms (F

and F

) for each ionizable compound

were carefully calculated according to the pH of the donor solution used. As for the donor

solvent containing no buffer salt, the degree of ionization was derived from pK

and

concentration of solute. With compounds that are partially ionized/neutral and have known

values of the fraction ionized and neutral, F

and F

, we separate the experimental (total) value

of K

(t) into K

(n) for neutral and K

(i) for ionic species through the equation

Kp

(t) = K

(n) × F

+ K

(i) × F

Then we estimate K

(n) and K

(i) using our previously established LFER equation (Zhang et al.,

2012) and the neutral and ionic descriptors, and can obtain an approximation of the ratio

K

(n)/K

(i).

From K

(n)/K

(i) and the accurate values of F

and F

, the values of K

(n) and K

(i)

of partially ionized compounds are deduced. These values are included in Table 2.

RESULTS AND DISCUSSION

We surveyed the literature and collected in vitro log K

data of compounds recently measured,

especially compounds that were ionized under the experimental conditions. As the major

data sources, our previous dataset (Zhang et al., 2012) and the dataset of Baba et al. (2015).

were combined in the present work. For compounds that exist in both datasets, we took the

log K

values in our previous dataset. This is because most of our log K

values were derived

from Abraham and Martins (2004), who had adjusted log K

for ionization and temperature

8

original experimental conditions and b) their descriptors cannot be obtained from the

experimental data listed in the current literature. We also used compounds whose log K

had

been measured by ourselves under reliable experimental conditions. Descriptors for all the

neutral compounds and ionic species that we considered are listed in Table 2, together with

the corresponding values of log K

, corrected to 37 ℃. The values of log K

of the 247

compounds or species in our data set covers both ‘highly permeable’ and ‘poorly permeable’

values, varying from -10.01 to -3.00, and meets a normal distribution very well, with a mean

of -6.027 and a standard deviation of 1.165, as seen in Figure 1.

9

Table 2. Compounds and species used in this work, their solute descriptors, observed log K

values, and log K

values calculated from Eq. 6

No. Compounds E S A B V J+ _J- _{Inter Full} log Kp

(obs)

log Kp

(calc) Ref.

b

1 1,1-dichloropropanone 0.395 0.73 0.09 0.35 0.7918 0.0000 0.0000 1.0 0.0 -5.03 -4.83 Baba et al.,

2015

2 1-hexyl-2-pyrrolidone 0.407 1.05 0.00 0.75 1.5245 0.0000 0.0000 1.0 0.0 -5.21 -4.99 Baba et al.,

2015

3 1-methoxy-2-propanol 0.218 0.53 0.33 0.81 0.7896 0.0000 0.0000 1.0 0.0 -6.20 -6.28 Baba et al.,

2015

4 1-octyl-2-pyrrolidone 0.390 1.05 0.00 0.75 1.8063 0.0000 0.0000 1.0 0.0 -4.83 -4.48 Baba et al.,

2015

5 2,4,6-trichlorophenol 1.010 0.80 0.60 0.15 1.1423 0.0000 0.0000 1.0 0.0 -4.30 -4.19 Baba et al.,

2015

6 2,4-dichlorophenol 0.960 0.82 0.54 0.17 1.0199 0.0000 0.0000 1.0 0.0 -4.30 -4.45 Baba et al.,

2015

7 2-amino-4-nitrophenol 1.415 1.95 1.01 0.43 1.0491 0.0000 0.0000 1.0 0.0 -6.54 -5.81 Baba et al.,

2015

8 2-chlorophenol 0.853 0.88 0.32 0.31 0.8975 0.0000 0.0000 1.0 0.0 -4.56 -4.99 Zhang et al.,

2012

9 2-ethoxyethanol 0.237 0.55 0.29 0.82 0.7896 0.0000 0.0000 1.0 0.0 -6.68 -6.30 Zhang et al.,

2012

10 2-hydroxypropyl nicotinate 0.840 1.38 0.35 1.19 1.3720 0.0000 0.0000 1.0 0.0 -7.55 -6.59 Zhang et al.,

2012

11 2-naphthol 1.520 1.08 0.61 0.40 1.1441 0.0000 0.0000 1.0 0.0 -4.65 -4.89 Zhang et al.,

2012

12 2-nitro-p-phenylenediamine 1.525 2.05 0.35 0.70 1.0902 0.0000 0.0000 1.0 0.0 -6.66 -6.21 Baba et al.,

2015

13 2-phenylethanol 0.811 0.82 0.31 0.66 1.0569 0.0000 0.0000 1.0 0.0 -5.20 -5.52 Zhang et al.,

2012

14 3,4-xylenol 0.830 0.90 0.55 0.38 1.0569 0.0000 0.0000 1.0 0.0 -4.52 -4.97 Zhang et al.,

2012

15 3-methylphenol 0.822 0.88 0.57 0.34 0.9160 0.0000 0.0000 1.0 0.0 -4.89 -5.12 Zhang et al.,

2012

16 3-nitrophenol 1.050 1.57 0.79 0.23 0.9493 0.0000 0.0000 1.0 0.0 -5.33 -5.25 Baba et al.,

10

17 4-amino-2-nitrophenol 1.360 1.50 0.30 0.66 1.0491 0.0000 0.0000 1.0 0.0 -5.91 -5.87 Baba et al.,

2015

18 4-bromophenol 1.080 1.17 0.67 0.20 0.9501 0.0000 0.0000 1.0 0.0 -4.52 -4.89 Zhang et al.,

2012

19 4-butylphenol 0.796 0.88 0.55 0.37 1.3387 0.0000 0.0000 1.0 0.0 -4.47 -4.43 Baba et al.,

2015

20 4-chloro-3,5-dimethylphenol 0.925 0.96 0.64 0.21 1.1793 0.0000 0.0000 1.0 0.0 -4.31 -4.39 Zhang et al.,

2012

21 4-chloro-3-methylphenol 0.920 1.02 0.67 0.22 1.0384 0.0000 0.0000 1.0 0.0 -4.34 -4.71 Zhang et al.,

2012

22 4-chloro-m-phenylenediamine 1.358 1.50 0.23 0.69 1.0384 0.0000 0.0000 1.0 0.0 -6.54 -5.93 Zhang et al.,

2012

23 4-chlorophenol 0.915 1.08 0.67 0.20 0.8975 0.0000 0.0000 1.0 0.0 -4.52 -4.95 Zhang et al.,

2012

24 4-cyanophenol 0.940 1.63 0.80 0.29 0.9298 0.0000 0.0000 1.0 0.0 -5.53 -5.49 Baba et al.,

2015

25 4-ethylphenol 0.800 0.90 0.55 0.36 1.0569 0.0000 0.0000 1.0 0.0 -4.53 -4.92 Zhang et al.,

2012

26 4-hydroxybenzyl alcohol 0.998 1.30 0.86 0.79 0.9747 0.0000 0.0000 0.0 0.0 -6.26 -6.43 Zhang et al.,

2012 27 4-hydroxy-methylphenylacetate 0.908 1.46 0.59 0.68 1.2722 0.0000 0.0000 1.0 0.0 -5.26 -5.65 Zhang et al.,

2012

28 4-hydroxyphenylacetamide 1.180 2.08 0.84 0.94 1.1724 0.0000 0.0000 0.0 0.0 -6.89 -6.88 Zhang et al.,

2012

29 4-hydroxyphenylacetic acid 1.030 1.45 0.94 0.74 1.1313 0.0000 0.0000 0.0 0.0 -6.16 -6.14 Baba et al.,

2015 30 4-MeC6H4CH2NH(CH2)4Me, cation 0.610 2.60 1.34 0.00 1.8240 1.3136 0.0000 1.0 0.0 -5.80 -5.94 Zhang et al.,

2012 31 4-MeC6H4CH2NH(CH2)5Me, cation 0.600 2.60 1.36 0.00 1.9649 1.2956 0.0000 1.0 0.0 -5.67 -5.67 Zhang et al.,

2012 32 4-MeC6H4CH2NH(CH2)6Me, cation 0.590 2.63 1.36 0.00 2.1058 1.2969 0.0000 1.0 0.0 -5.50 -5.43 Zhang et al.,

2012

33 4-MeC6H4CH2NHBu, cation 0.620 2.62 1.34 0.00 1.6831 1.3349 0.0000 1.0 0.0 -6.52 -6.23 Zhang et al.,

2012

34 4-MeC6H4CH2NHEt, cation 0.640 2.66 1.44 0.00 1.4013 1.2994 0.0000 1.0 0.0 -6.77 -6.74 Zhang et al.,

11

35 4-MeC6H4CH2NHMe, cation 0.650 2.58 1.42 0.00 1.2604 1.2835 0.0000 1.0 0.0 -7.51 -6.92 Zhang et al.,

2012

36 4-MeC6H4CH2NHPr, cation 0.630 2.63 1.37 0.00 1.5422 1.3290 0.0000 1.0 0.0 -6.77 -6.49 Zhang et al.,

2012

37 4-nitrophenol 1.070 1.72 0.82 0.26 0.9493 0.0000 0.0000 1.0 0.0 -5.33 -5.42 Baba et al.,

2015

38 4-propoxyphenol 0.840 1.17 0.57 0.52 1.2565 0.0000 0.0000 1.0 0.0 -5.18 -5.12 Baba et al.,

2015

39 5,5-diethylbarbituric acid 1.030 1.14 0.47 1.18 1.3739 0.0000 0.0000 1.0 0.0 -7.29 -6.43 Zhang et al.,

2012 40 5-ethyl-5-(3-methylbutyl)barbital 1.030 1.11 0.47 1.23 1.7966 0.0000 0.0000 1.0 0.0 -5.98 -5.77 Zhang et al.,

2012 41 5-ethyl-5-butylbarbituric acid 1.030 1.14 0.47 1.18 1.6557 0.0000 0.0000 1.0 0.0 -7.05 -5.92 Zhang et al.,

2012

42 5-ethyl-5-phenylbarbital 1.630 1.80 0.73 1.15 1.6999 0.0000 0.0000 1.0 0.0 -6.68 -6.17 Zhang et al.,

2012

43 5-fluorouracil 0.720 0.84 0.57 1.02 0.7693 0.0000 0.0000 1.0 0.0 -6.82 -7.02 Zhang et al.,

2012

44 8-methoxypsoralen 1.611 1.70 0.00 0.80 1.4504 0.0000 0.0000 1.0 0.0 -5.12 -5.47 Zhang et al.,

2012

45 acetic acid 0.265 0.64 0.62 0.44 0.4648 0.0000 0.0000 1.0 0.0 -6.08 -6.12 Baba et al.,

2015

46 acetylsalicylic acid 0.781 1.69 0.71 0.67 1.2879 0.0000 0.0000 0.0 1.0 -5.50 -5.79 Baba et al.,

2015

47 aldosterone 2.010 3.47 0.40 1.90 2.6890 0.0000 0.0000 1.0 0.0 -7.45 -7.06 Zhang et al.,

2012 48 alprenolol, neutral, Fn = 0.02, log Kp(t) = -6.90 1.250 1.09 0.15 1.44 2.16 0.0000 0.0000 1.0 0.0 -5.30 -5.48 Zhang et al.,

2012 49 alprenolol, cation, Fi = 0.98, log Kp(t) =-6.90 1.100 4.46 1.78 0.00 2.1802 2.2574 0.0000 1.0 0.0 -7.59 -7.90 Zhang et al.,

2012

50 aminopyrine 1.680 1.74 0.00 1.60 1.8662 0.0000 0.0000 0.0 1.0 -6.55 -6.68 Baba et al.,

2015

51 amylobarbital 1.030 1.10 0.59 1.22 1.7966 0.0000 0.0000 0.0 1.0 -6.00 -5.78 Baba et al.,

2015

52 aniline 0.955 0.96 0.26 0.41 0.8162 0.0000 0.0000 1.0 0.0 -4.94 -5.39 Baba et al.,

12

53 anisole 0.708 0.75 0.00 0.29 0.9160 0.0000 0.0000 1.0 0.0 -4.41 -4.74 Baba et al.,

2015

54 atenolol 1.450 1.90 0.62 2.03 2.1763 0.0000 0.0000 1.0 0.0 -7.35 -7.50 Baba et al.,

2015

55 barbital 1.030 1.00 0.58 1.12 1.3739 0.0000 0.0000 0.0 1.0 -7.31 -6.24 Baba et al.,

2015

56 benzaldehyde 0.820 1.00 0.00 0.39 0.8730 0.0000 0.0000 1.0 0.0 -4.51 -5.20 Baba et al.,

2015

57 benzene 0.610 0.52 0.00 0.14 0.7164 0.0000 0.0000 1.0 0.0 -4.27 -4.61 Zhang et al.,

2012

58 benzenetriol 1.180 1.37 1.40 0.68 0.8925 0.0000 0.0000 1.0 0.0 -6.98 -6.51 Baba et al.,

2015

59 benzoic acid 0.730 0.90 0.59 0.40 0.9317 0.0000 0.0000 1.0 0.0 -5.68 -5.27 Baba et al.,

2015

60 benzyl alcohol 0.803 0.87 0.39 0.56 0.9160 0.0000 0.0000 1.0 0.0 -5.30 -5.59 Zhang et al.,

2012

61 benzyl nicotinate 1.262 1.60 0.00 0.80 1.6393 0.0000 0.0000 1.0 0.0 -4.87 -5.12 Zhang et al.,

2012

62 betamethasone 2.040 3.51 0.71 1.92 2.9132 0.0000 0.0000 1.0 0.0 -7.15 -6.83 Baba et al.,

2015

63 betamethasone-17-valerate 1.970 3.10 0.56 2.40 3.6334 0.0000 0.0000 1.0 0.0 -6.50 -6.42 Baba et al.,

2015 64 bromoacetic acid Fi = 0.70, log Kp(t) = -6.52 0.706 3.66 0.00 0.82 0.6183 0.0000 0.1469 1.0 0.0 -8.01 -7.96 Baba et al.,

2015 65 bromoacetic acid Fn = 0.30 log Kp(t) = -6.52 0.556 1.06 0.77 0.38 0.6398 0.0000 0.0000 1.0 0.0 -6.01 -5.92 Baba et al.,

2015 66 bromochloroacetic acid Fi =0.90, log Kp(t) =-6.46 0.790 3.18 0.10 2.48 0.7407 0.0000 1.9889 1.0 0.0 -6.82 -6.95 Baba et al.,

2015 67 bromochloroacetic acid Fn = 0.10, log Kp(t) = -6.46 0.640 1.24 0.92 0.28 0.7622 0.0000 0.0000 1.0 0.0 -5.67 -5.61 Baba et al.,

2015

68 bromochloroacetonitrile 0.597 1.10 0.22 0.21 0.7016 0.0000 0.0000 1.0 0.0 -4.35 -5.23 Baba et al.,

2015

69 bromodichloromethane 0.593 0.69 0.10 0.04 0.6693 0.0000 0.0000 1.0 0.0 -4.41 -4.59 Baba et al.,

2015

70 butan-1-ol 0.224 0.42 0.37 0.48 0.7309 0.0000 0.0000 1.0 0.0 -5.70 -5.53 Zhang et al.,

13

71 butan-2,3-diol 0.341 0.93 0.61 0.88 0.7896 0.0000 0.0000 1.0 0.0 -7.38 -6.77 Zhang et al.,

2012

72 butan-2-one 0.166 0.70 0.00 0.51 0.6879 0.0000 0.0000 1.0 0.0 -5.42 -5.73 Zhang et al.,

2012

73 butanoic acid 0.210 0.64 0.61 0.45 0.7466 0.0000 0.0000 0.0 0.0 -6.41 -5.64 Baba et al.,

2015

74 butobarbital 1.030 1.14 0.47 1.18 1.6557 0.0000 0.0000 0.0 1.0 -7.07 -5.92 Baba et al.,

2015

75 butoxyethanol 0.201 0.53 0.26 0.83 1.0714 0.0000 0.0000 1.0 0.0 -6.00 -5.80 Baba et al.,

2015

76 butyl nicotinate 0.658 1.07 0.00 0.73 1.4542 0.0000 0.0000 1.0 0.0 -4.86 -5.04 Zhang et al.,

2012

77 butyl p-aminobenzoate 1.010 1.35 0.30 0.68 1.5951 0.0000 0.0000 1.0 0.0 -4.41 -4.89 Baba et al.,

2015

78 butyl paraben 0.900 1.47 0.74 0.43 1.5540 0.0000 0.0000 1.0 0.0 -4.34 -4.59 Akomeah et

al., 2007

79 C6H5(CH2)2COOH 0.750 1.18 0.60 0.60 1.2135 0.0000 0.0000 1.0 0.0 -4.93 -5.42 Zhang et al.,

2012 80 C6H5(CH2)2COOH, anion 0.900 3.43 0.03 3.02 1.1920 0.0000 2.1879 1.0 0.0 -6.78 -7.07 Zhang et al.,

2012

81 C6H5(CH2)3COOH 0.760 1.29 0.61 0.57 1.3544 0.0000 0.0000 1.0 0.0 -4.85 -5.16

Zhang et al., 2012 82 C6H5(CH2)3COOH, anion 0.910 3.59 0.04 3.01 1.3329 0.0000 2.2184 1.0 0.0 -6.70 -6.82 Zhang et al.,

2012

83 C6H5(CH2)4COOH 0.770 1.24 0.57 0.60 1.4933 0.0000 0.0000 1.0 0.0 -4.30 -4.94 Zhang et al.,

2012 84 C6H5(CH2)4COOH, anion 0.920 3.63 0.04 3.10 1.4718 0.0000 2.2794 1.0 0.0 -6.15 -6.66 Zhang et al.,

2012

85 C6H5(CH2)7COOH 0.790 1.27 0.57 0.62 1.7771 0.0000 0.0000 1.0 0.0 -3.86 -4.49 Zhang et al.,

2012 86 C6H5(CH2)7COOH, anion 0.940 3.87 0.07 3.26 1.8965 0.0000 2.4256 1.0 0.0 -5.71 -6.07 Zhang et al.,

2012

87 C6H5COOH 0.730 0.90 0.59 0.40 0.9317 0.0000 0.0000 1.0 0.0 -4.91 -5.27 Zhang et al.,

2012

88 C6H5COOH, anion 0.880 3.05 0.02 2.75 0.9102 0.0000 2.1385 1.0 0.0 -6.76 -6.81 Zhang et al.,

14

89 caffeine 1.500 1.82 0.08 1.25 1.3632 0.0000 0.0000 1.0 0.0 -6.85 -6.83 Akomeah et

al., 2007

90 catechol 0.970 1.10 0.88 0.47 0.8338 0.0000 0.0000 1.0 0.0 -5.87 -5.80 Baba et al.,

2015

91 chloral hydrate 0.814 0.96 0.59 0.56 0.8750 0.0000 0.0000 1.0 0.0 -5.97 -5.78 Baba et al.,

2015 92 chloroacetic acid, Fi = 0.90, log Kp(t) = -6.62 0.577 2.94 0.00 1.10 0.5657 0.0000 0.3680 1.0 0.0 -7.78 -7.77 Baba et al.,

2015 93 chloroacetic acid, Fn = 0.1, log Kp(t) = -6.62 0.427 1.03 0.79 0.35 0.5872 0.0000 0.0000 1.0 0.0 -5.97 -5.95 Baba et al.,

2015

94 chloroacetonitrile 0.372 0.89 0.38 0.26 0.5266 0.0000 0.0000 1.0 0.0 -4.56 -5.63 Baba et al.,

2015

95 chlorodibromomethane 0.775 0.68 0.12 0.10 0.7219 0.0000 0.0000 1.0 0.0 -4.37 -4.62 Baba et al.,

2015

96 chlorpheniramine 1.465 1.41 0.00 1.33 2.2098 0.0000 0.0000 0.0 1.0 -5.93 -5.24 Baba et al.,

2015

97 codeine 2.220 2.15 0.15 1.80 2.2057 0.0000 0.0000 1.0 0.0 -6.57 -6.78 Zhang et al.,

2012

98 codeine cation 2.070 5.83 2.68 0.00 2.2272 2.9847 0.0000 0.0 0.0 -10.01 -9.90 Roy and

Flynn, 1989

99 cortexolone 1.910 3.45 0.36 1.60 2.7389 0.0000 0.0000 1.0 0.0 -7.20 -6.23 Baba et al.,

2015

100 cortexone 1.740 3.50 0.14 1.31 2.6802 0.0000 0.0000 1.0 0.0 -6.42 -5.61 Baba et al.,

2015

101 corticosterone 1.860 3.43 0.40 1.63 2.7389 0.0000 0.0000 1.0 0.0 -6.84 -6.31 Zhang et al.,

2012

102 cortisone 1.960 3.50 0.36 1.87 2.7546 0.0000 0.0000 1.0 0.0 -7.38 -6.88 Baba et al.,

2015

103 coumarin 1.230 1.68 0.00 0.52 1.0619 0.0000 0.0000 0.0 1.0 -5.60 -5.53 Baba et al.,

2015

104 cyclobarbitone 1.440 1.35 0.49 1.45 1.7859 0.0000 0.0000 0.0 1.0 -6.65 -6.42 Baba et al.,

2015

105 cytarabine 2.090 2.25 0.87 2.12 1.6234 0.0000 0.0000 1.0 0.0 -8.66 -8.92 Baba et al.,

2015

106 decan-1-ol 0.191 0.42 0.37 0.48 1.5763 0.0000 0.0000 1.0 0.0 -4.15 -4.01 Zhang et al.,

15

107 dexamethasone 2.040 3.51 0.71 1.92 2.9132 0.0000 0.0000 0.0 0.0 -7.27 -6.83 Zhang et al.,

2012

108 diazinon 1.310 1.55 0.00 1.40 2.3056 0.0000 0.0000 1.0 0.0 -5.62 -5.34 Baba et al.,

2015 109 dibromoacetic acid, Fi = 0.85, log Kp(t) = -6.25 0.948 3.34 0.11 2.53 0.7955 0.0000 2.0502 1.0 0.0 -6.76 -6.90

Baba et al., 2015 110 dibromoacetic acid, Fn = 0.15, log Kp(t) =-6.25 0.798 1.24 0.92 0.31 0.8147 0.0000 0.0000 1.0 0.0 -5.57 -5.57 Baba et al.,

2015

111 dibromoacetonitrile 0.766 1.24 0.25 0.26 0.7542 0.0000 0.0000 1.0 0.0 -4.33 -5.33 Baba et al.,

2015 112 dichloroacetic acid, Fi = 0.80, log Kp(t) = -6.39 0.632 2.53 0.00 2.18 0.6881 0.0000 1.4260 1.0 0.0 -7.21 -7.30 Baba et al.,

2015 113 dichloroacetic acid, Fn = 0.20, log Kp(t) = -6.39 0.482 1.20 0.92 0.26 0.7096 0.0000 0.0000 1.0 0.0 -5.75 -5.65 Baba et al.,

2015

114 dichloroacetonitrile 0.428 0.96 0.20 0.17 0.6490 0.0000 0.0000 1.0 0.0 -4.38 -5.16 Baba et al.,

2015

115 diclofenac 1.810 1.85 0.55 0.77 2.0250 0.0000 0.0000 1.0 0.0 -5.30 -4.61 Zhang et al.,

2012

116 diclofenac, anion 1.960 5.31 0.03 3.35 2.0035 0.0000 2.6243 1.0 0.0 -7.00 -6.32 Zhang et al.,

2012

117 diethylcarbamazine 0.645 1.30 0.00 1.55 1.7241 0.0000 0.0000 1.0 0.0 -6.15 -6.69 Zhang et al.,

2012

118 diethylether 0.041 0.25 0.00 0.45 0.7309 0.0000 0.0000 1.0 0.0 -5.37 -5.25 Zhang et al.,

2012

119 digitoxin 3.460 5.63 1.33 4.35 5.6938 0.0000 0.0000 1.0 0.0 -8.15 -9.03 Zhang et al.,

2012

120 dihydrocodeine 2.060 2.32 0.26 1.74 2.2487 0.0000 0.0000 1.0 0.0 -6.00 -6.72 Zhang et al.,

2012

121 dihydromorphine 2.080 1.35 0.42 2.04 2.1078 0.0000 0.0000 1.0 0.0 -7.58 -7.16 Zhang et al.,

2012

122 dimethylethylamine 0.094 0.18 0.00 0.64 0.7720 0.0000 0.0000 1.0 0.0 -5.80 -5.59 Baba et al.,

2015

123 ephedrine 0.916 0.74 0.21 1.21 1.4385 0.0000 0.0000 0.0 1.0 -5.50 -6.07 Baba et al.,

2015

124 estradiol 1.800 1.77 0.86 1.10 2.1988 0.0000 0.0000 1.0 0.0 -5.61 -5.16 Zhang et al.,

16

125 estrone 1.730 2.05 0.50 1.08 2.1558 0.0000 0.0000 1.0 0.0 -5.52 -5.24 Baba et al.,

2015

126 ethacrynic acid anion 1.500 4.91 0.07 3.65 2.0318 0.0000 2.5114 1.0 0.0 -7.38 -7.12 Baba et al.,

2015

127 ethanol 0.246 0.42 0.37 0.48 0.4491 0.0000 0.0000 1.0 0.0 -6.08 -6.03 Zhang et al.,

2012

128 ethyl nicotinate 0.667 1.10 0.00 0.73 1.1724 0.0000 0.0000 1.0 0.0 -5.28 -5.57 Zhang et al.,

2012

129 ethyl p-aminobenzoate 1.030 1.31 0.31 0.69 1.3133 0.0000 0.0000 1.0 0.0 -5.06 -5.40 Baba et al.,

2015

130 ethylbenzene 0.613 0.51 0.00 0.15 0.9982 0.0000 0.0000 1.0 0.0 -3.00 -4.12 Zhang et al.,

2012 131 ethylene glycol mono isopropyl ether 0.196 0.48 0.21 0.91 0.9305 0.0000 0.0000 1.0 0.0 -6.71 -6.20 Baba et al.,

2015 132 ethylene glycol mono methyl ether acetate 0.166 0.79 0.00 0.81 0.9462 0.0000 0.0000 1.0 0.0 -6.10 -6.05 Baba et al.,

2015 133 ethylene glycol mono propyl ether 0.212 0.50 0.30 0.83 0.9305 0.0000 0.0000 1.0 0.0 -6.34 -6.05 Baba et al.,

2015

134 etodolac 1.803 2.17 1.05 1.15 2.2390 0.0000 0.0000 0.0 1.0 -5.48 -5.51 Baba et al.,

2015

135 famotidine 2.690 2.14 1.20 2.50 2.2617 0.0000 0.0000 0.0 1.0 -8.15 -8.66 Baba et al.,

2015

136 fentanyl 1.830 1.75 0.00 1.81 2.8399 0.0000 0.0000 1.0 0.0 -5.81 -5.42 Baba et al.,

2015

137 fentanyl cation 1.680 5.67 2.22 0.00 2.8615 2.8615 0.0000 0.0 0.0 -8.21 -8.38 Roy and

Flynn, 1990

138 fluocinonide 1.950 2.48 0.31 2.51 3.4603 0.0000 0.0000 1.0 0.0 -6.33 -6.54 Zhang et al.,

2012 139 flurbiprofen, neutral, Fn = 0.01, log Kp(t) = -6.20 1.440 1.45 0.62 0.76 1.84 0.0000 0.0000 1.0 0.0 -4.72 -4.75 Zhang et al.,

2012 140 flurbiprofen, anion, Fi = 0.99, log Kp(t) = -6.20 1.590 4.56 0.07 3.36 1.8174 0.0000 2.5383 1.0 0.0 -6.36 -6.51 Zhang et al.,

2012

141 flurbiprofen glucoside 2.321 3.80 0.85 1.80 2.8693 0.0000 0.0000 1.0 0.0 -6.28 -6.80 Swart et al.,

2005

142 flurbiprofen mannoside 2.321 3.73 0.85 1.95 2.8693 0.0000 0.0000 1.0 0.0 -6.74 -7.13 Swart et al.,

17

143 glycerol trinitrate 0.586 2.11 0.00 0.35 1.2300 0.0000 0.0000 1.0 0.0 -5.21 -5.16 Zhang et al.,

2012

144 griseofulvin 1.750 2.64 0.00 1.44 2.3947 0.0000 0.0000 0.0 1.0 -6.44 -5.87 Baba et al.,

2015

145 heptan-1-ol 0.211 0.42 0.37 0.48 1.1536 0.0000 0.0000 0.0 0.0 -4.57 -4.77 Zhang et al.,

2012

146 heptanoic acid 0.149 0.64 0.62 0.44 1.1693 0.0000 0.0000 0.0 0.0 -5.26 -4.87 Baba et al.,

2015

147 hexan-1-ol 0.210 0.42 0.37 0.48 1.0127 0.0000 0.0000 1.0 0.0 -4.92 -5.02 Zhang et al.,

2012

148 hexanoic acid 0.174 0.63 0.62 0.44 1.0284 0.0000 0.0000 0.0 0.0 -5.48 -5.11 Baba et al.,

2015

149 hexyl nicotinate 0.628 1.07 0.00 0.73 1.7360 0.0000 0.0000 1.0 0.0 -4.83 -4.54 Zhang et al.,

2012

150 hydrocodone 2.030 1.81 0.00 1.85 2.2057 0.0000 0.0000 1.0 0.0 -6.26 -6.67 Zhang et al.,

2012

151 hydrocortisone 2.030 3.49 0.71 1.90 2.7976 0.0000 0.0000 1.0 0.0 -7.22 -6.98 Zhang et al.,

2012 152 hydrocortisone hemipimelate 2.020 3.58 1.06 2.61 3.8740 0.0000 0.0000 0.0 0.0 -6.24 -6.94 Zhang et al.,

2012 153 hydrocortisone hemisuccinate 2.100 3.15 1.06 2.61 3.4513 0.0000 0.0000 0.0 0.0 -6.69 -7.43 Zhang et al.,

2012

154 hydrocortisone hexanoate 1.810 3.02 0.46 2.16 3.6587 0.0000 0.0000 0.0 0.0 -5.30 -5.73 Zhang et al.,

2012 155 hydrocortisone hydroxyhexanoate 2.020 3.49 0.83 2.64 3.7174 0.0000 0.0000 0.0 0.0 -6.60 -7.17 Zhang et al.,

2012 156 hydrocortisone methylpimelate 1.930 3.49 0.46 2.61 4.0149 0.0000 0.0000 0.0 0.0 -5.82 -6.45 Zhang et al.,

2012 157 hydrocortisone methylsuccinate 1.990 3.11 0.46 2.61 3.5922 0.0000 0.0000 0.0 0.0 -7.23 -6.97 Zhang et al.,

2012 158 hydrocortisone N,N-dimethylsuccinate 2.210 3.77 0.46 2.86 3.7742 0.0000 0.0000 0.0 0.0 -7.73 -7.62 Zhang et al.,

2012

159 hydrocortisone octanoate 1.770 3.05 0.46 2.16 3.9405 0.0000 0.0000 0.0 0.0 -4.76 -5.24 Zhang et al.,

2012

160 hydrocortisone pimelamate 2.210 4.15 0.96 2.78 3.9151 0.0000 0.0000 0.0 0.0 -6.61 -7.57 Zhang et al.,

2012 161 hydrocortisone propionate 1.870 2.90 0.46 2.16 3.2360 0.0000 0.0000 0.0 0.0 -6.02 -6.41 Zhang et al.,

18 162 hydrocortisone succinamate 2.310 3.32 1.01 2.84 3.4924 0.0000 0.0000 0.0 0.0 -8.14 -7.98 Zhang et al.,

2012

163 hydromorphone 2.040 1.60 0.16 1.95 2.0648 0.0000 0.0000 1.0 0.0 -7.83 -7.09 Zhang et al.,

2012

164 hydroquinone 1.063 1.27 1.06 0.57 0.8338 0.0000 0.0000 1.0 0.0 -6.31 -6.19 Baba et al.,

2015

165 hydroxypregnenolone 1.550 3.35 0.57 1.35 2.7232 0.0000 0.0000 1.0 0.0 -6.30 -5.71 Baba et al.,

2015

166 hydroxyprogesterone 1.640 3.35 0.25 1.31 2.6802 0.0000 0.0000 1.0 0.0 -6.30 -5.57 Baba et al.,

2015 167 ibuprofen, neutral, Fn = 0.03, log Kp(t) = -5.83 0.730 0.70 0.57 0.79 1.7771 0.0000 0.0000 1.0 0.0 -4.58 -4.57 Zhang et al.,

2012 168 ibuprofen, anion , Fi = 0.97, log Kp(t) = -5.83 0.880 3.50 0.08 3.31 1.7556 0.0000 2.4188 1.0 0.0 -6.15 -6.25 Zhang et al.,

2012

169 ibuprofen glucoside 1.826 3.11 0.85 2.00 2.8075 0.0000 0.0000 1.0 0.0 -6.94 -7.05 Swart et al.,

2005

170 ibuprofen mannoside 1.826 2.79 0.85 2.00 2.8075 0.0000 0.0000 1.0 0.0 -6.55 -6.86 Swart et al.,

2005

171 indomethacin 2.240 1.47 0.58 1.43 2.5299 0.0000 0.0000 1.0 0.0 -5.39 -5.03 Zhang et al.,

2012

172 indomethacin anion 2.390 5.62 0.10 4.38 2.5084 0.0000 2.9899 1.0 0.0 -7.22 -7.17 Zhang et al.,

2012

173 isoquinoline 1.211 1.00 0.00 0.54 1.0443 0.0000 0.0000 0.0 1.0 -5.11 -5.20 Zhang et al.,

2012

174 iso-thymol 0.824 0.81 0.56 0.43 1.3387 0.0000 0.0000 1.0 0.0 -4.84 -4.53 Baba et al.,

2015 175 ketoprofen, neutral, Fn = 0.50, logKp(t) = -5.51 1.650 2.26 0.55 0.89 1.9779 0.0000 0.0000 1.0 0.0 -5.22 -5.26 Zhang et al.,

2012 176 ketoprofen, anion, Fi = 0.50, logKp(t) = -5.51 1.800 5.49 0.01 3.39 1.9564 0.0000 2.4851 1.0 0.0 -6.84 -6.97 Zhang et al.,

2012

177 ketoprofen glucoside 2.628 4.22 0.85 2.20 3.0082 0.0000 0.0000 1.0 0.0 -7.73 -7.74 Swart et al.,

2005

178 ketoprofen mannoside 2.628 4.07 0.85 2.20 3.0082 0.0000 0.0000 1.0 0.0 -7.59 -7.65 Swart et al.,

2005

179 ketorolac 1.600 2.03 0.65 1.05 1.8712 0.0000 0.0000 1.0 0.0 -5.60 -5.74 Baba et al.,

2015

180 levosimendan 2.100 1.76 0.70 1.60 2.0915 0.0000 0.0000 1.0 0.0 -6.00 -6.46 Baba et al.,

19

181 lidocaine 1.110 1.51 0.07 1.24 2.0589 0.0000 0.0000 1.0 0.0 -5.51 -5.42 Baba et al.,

2015

182 lidocaine cation 0.960 4.18 2.12 0.00 2.0804 1.7490 0.0000 1.0 0.0 -7.42 -7.29 Baba et al.,

2015

183 linolenic acid anion 0.698 3.59 0.14 3.90 2.5687 0.0000 2.6821 1.0 0.0 -5.99 -5.67 Baba et al.,

2015

184 mannitol 0.836 2.33 0.87 1.77 1.3062 0.0000 0.0000 1.0 0.0 -8.42 -8.86 Zhang et al.,

2012

185 m-cresol 0.822 0.88 0.57 0.34 0.9160 0.0000 0.0000 1.0 0.0 -4.89 -5.12 Zhang et al.,

2012

186 meperidine cation 0.840 4.25 1.93 0.00 2.0716 1.8235 0.0000 1.0 0.0 -7.43 -7.41 Baba et al.,

2015

187 methanol 0.278 0.44 0.43 0.47 0.3082 0.0000 0.0000 1.0 0.0 -6.38 -6.29 Zhang et al.,

2012 188 methyl 4-hydroxyphenylacetate 0.908 1.36 0.59 0.70 1.2722 0.0000 0.0000 0.0 0.0 -5.26 -5.64 Baba et al.,

2015

189 methyl nicotinate 0.710 1.13 0.00 0.71 1.0315 0.0000 0.0000 1.0 0.0 -5.77 -5.78 Zhang et al.,

2012

190 methyl p-aminobenzoate 1.030 1.25 0.30 0.72 1.1724 0.0000 0.0000 1.0 0.0 -4.99 -5.68 Baba et al.,

2015

191 methyl paraben 0.930 1.46 0.71 0.46 1.1313 0.0000 0.0000 1.0 0.0 -5.03 -5.41 Akomeah et

al., 2007

192 methyl salicylate 0.850 0.84 0.02 0.47 1.1313 0.0000 0.0000 1.0 0.0 -4.80 -4.83 Baba et al.,

2015

193 methylphenylether 0.708 0.75 0.00 0.29 0.9160 0.0000 0.0000 1.0 0.0 -4.68 -4.74 Zhang et al.,

2012

194 methyltriglycol nicotinate 0.730 1.42 0.00 1.79 2.0530 0.0000 0.0000 1.0 0.0 -6.83 -6.74 Zhang et al.,

2012

195 morphine 2.230 1.30 0.39 2.01 2.0648 0.0000 0.0000 1.0 0.0 -7.24 -7.11 Zhang et al.,

2012

196 naproxen 1.510 2.02 0.60 0.67 1.7821 0.0000 0.0000 1.0 0.0 -4.97 -4.97 Zhang et al.,

2012

197 naproxen, anion 1.660 5.07 0.02 3.11 1.7606 0.0000 2.4260 1.0 0.0 -6.53 -6.56 Zhang et al.,

2012

198 naproxen glucoside 2.818 3.81 0.85 2.10 2.8124 0.0000 0.0000 1.0 0.0 -7.89 -7.57 Swart et al.,

2005

199 naproxen mannoside 2.818 3.73 0.85 2.10 2.8124 0.0000 0.0000 1.0 0.0 -7.70 -7.52 Swart et al.,

20

200 nicorandil 1.100 2.60 0.39 1.28 1.4464 0.0000 0.0000 0.0 1.0 -7.30 -7.39 Baba et al.,

2015

201 nicotine 0.865 0.88 0.00 1.09 1.3710 0.0000 0.0000 1.0 0.0 -5.34 -5.92 Baba et al.,

2015

202 nimesulide 2.109 2.70 0.31 1.09 2.0787 0.0000 0.0000 0.0 1.0 -6.35 -5.68 Baba et al.,

2015

203 nizatidine 1.910 2.92 0.64 2.41 2.4622 0.0000 0.0000 0.0 1.0 -7.78 -8.47 Baba et al.,

2015

204 nonan-1-ol 0.193 0.42 0.37 0.48 1.4354 0.0000 0.0000 1.0 0.0 -4.30 -4.27 Zhang et al.,

2012

205 o-cresol 0.840 0.86 0.52 0.30 0.9160 0.0000 0.0000 1.0 0.0 -4.88 -4.99 Zhang et al.,

2012

206 octan-1-ol 0.199 0.42 0.37 0.48 1.2945 0.0000 0.0000 1.0 0.0 -4.30 -4.52 Zhang et al.,

2012

207 octanoic acid 0.150 0.65 0.62 0.45 1.3102 0.0000 0.0000 0.0 0.0 -5.18 -4.65 Baba et al.,

2015

208 o-phenylenediamine 1.260 1.40 0.24 0.73 0.9160 0.0000 0.0000 1.0 0.0 -6.70 -6.21 Zhang et al.,

2012

209 o-tert-butylphenol 0.823 0.92 0.52 0.40 1.3387 0.0000 0.0000 1.0 0.0 -4.48 -4.51 Baba et al.,

2015

210 ouabain 4.010 6.20 0.90 3.46 4.1615 0.0000 0.0000 1.0 0.0 -9.66 -9.75 Zhang et al.,

2012

211 oxycodone 2.320 2.50 0.29 1.91 2.2644 0.0000 0.0000 1.0 0.0 -6.43 -7.18 Zhang et al.,

2012

212 oxymorphone 2.320 2.10 0.39 1.90 2.1235 0.0000 0.0000 1.0 0.0 -7.60 -7.21 Zhang et al.,

2012

213 p-cresol 0.820 0.87 0.57 0.31 0.9160 0.0000 0.0000 1.0 0.0 -4.83 -5.04 Zhang et al.,

2012

214 pentan-1-ol 0.219 0.42 0.37 0.48 0.8718 0.0000 0.0000 0.0 0.0 -5.30 -5.28 Zhang et al.,

2012

215 pentanoic acid 0.205 0.63 0.62 0.45 0.8875 0.0000 0.0000 0.0 0.0 -6.11 -5.39 Baba et al.,

2015

216 phenobarbital 1.630 1.72 0.71 1.18 1.6999 0.0000 0.0000 0.0 1.0 -6.70 -6.19 Baba et al.,

2015

217 phenol 0.805 0.89 0.60 0.30 0.7751 0.0000 0.0000 1.0 0.0 -5.27 -5.29 Zhang et al.,

2012

218 phloroglucinol 1.360 1.39 1.40 0.73 0.8925 0.0000 0.0000 1.0 0.0 -5.87 -6.62 Baba et al.,

21

219 piroxicam, anion 2.710 6.81 0.00 3.78 2.2285 0.0000 2.7356 1.0 0.0 -7.50 -7.48 Zhang et al.,

2012

220 piroxicam, neutral 2.560 2.90 0.17 1.49 2.2500 0.0000 0.0000 1.0 0.0 -6.02 -6.36 Zhang et al.,

2012

221 p-phenylenediamine 1.300 1.66 0.44 0.83 0.9160 0.0000 0.0000 1.0 0.0 -6.98 -6.67 Zhang et al.,

2012

222 prednisolone 2.210 3.10 0.71 1.92 2.7546 0.0000 0.0000 1.0 0.0 -7.91 -6.85 Baba et al.,

2015

223 pregnenolone 1.360 3.29 0.32 1.18 2.6645 0.0000 0.0000 1.0 0.0 -5.90 -5.31 Baba et al.,

2015

224 progesterone 1.450 3.29 0.00 1.14 2.6215 0.0000 0.0000 1.0 0.0 -4.90 -5.17 Zhang et al.,

2012

225 propan-1-ol 0.236 0.42 0.37 0.48 0.5900 0.0000 0.0000 1.0 0.0 -5.93 -5.78 Zhang et al.,

2012 226 propranolol (Fn larger than 0.85) 1.840 1.43 0.44 1.31 2.1480 0.0000 0.0000 1.0 0.0 -6.05 -5.41 Baba et al.,

2015 227 propranolol, cation (Fi larger than 0.995) 1.690 4.31 2.07 0.00 2.1695 2.4319 0.0000 1.0 0.0 -7.70 -8.11 Zhang et al.,

2012

228 propylparaben 0.900 1.45 0.74 0.43 1.4131 0.0000 0.0000 1.0 0.0 -5.41 -4.83 Baba et al.,

2015

229 pyrogallol 1.165 1.26 1.35 0.64 0.8925 0.0000 0.0000 1.0 0.0 -6.17 -6.33 Baba et al.,

2015

230 ranitidine 1.600 1.63 0.25 2.33 2.3985 0.0000 0.0000 0.0 1.0 -7.41 -7.52 Baba et al.,

2015

231 resorcinol 0.980 1.11 1.09 0.52 0.8338 0.0000 0.0000 1.0 0.0 -6.70 -6.00 Zhang et al.,

2012

232 salicylic acid 0.900 0.85 0.73 0.37 0.9904 0.0000 0.0000 1.0 0.0 -5.07 -5.08 Zhang et al.,

2012

233 salicylic acid, anion 1.050 3.19 0.08 2.74 0.9689 0.0000 2.2641 1.0 0.0 -7.04 -6.45 Zhang et al.,

2012

234 scopolamine 1.686 1.32 0.09 2.17 2.2321 0.0000 0.0000 0.0 1.0 -7.58 -7.18 Baba et al.,

2015

235 sufentanil 1.800 2.28 0.00 1.91 3.1051 0.0000 0.0000 1.0 0.0 -5.53 -5.51 Baba et al.,

2015

236 sufentanil cation 1.650 6.16 3.02 0.00 3.1266 2.5848 0.0000 1.0 0.0 -8.11 -8.06 Baba et al.,

2015

237 testosterone 1.540 2.56 0.32 1.17 2.3827 0.0000 0.0000 1.0 0.0 -5.54 -5.33 Zhang et al.,

22

238 theophylline 1.500 1.60 0.54 1.34 1.2223 0.0000 0.0000 1.0 0.0 -6.92 -7.33 Baba et al.,

2015

239 thymol 0.822 0.80 0.43 0.44 1.3387 0.0000 0.0000 1.0 0.0 -4.35 -4.51 Zhang et al.,

2012

240 toluene 0.601 0.52 0.00 0.14 0.8573 0.0000 0.0000 0.0 0.0 -3.64 -4.36 Zhang et al.,

2012

241 tribromomethane 0.974 0.68 0.15 0.06 0.7745 0.0000 0.0000 1.0 0.0 -4.34 -4.41 Baba et al.,

2015 242 trichloroacetic acid, Fi = 0.90, log Kp(t) = -6.39 0.674 3.08 0.14 2.48 0.8105 0.0000 1.9882 1.0 0.0 -6.75 -6.80 Baba et al.,

2015 243 trichloroacetic acid, Fn= 0.10, log Kp(t) = -6.39 0.524 1.21 1.01 0.26 0.8320 0.0000 0.0000 1.0 0.0 -5.60 -5.46 Baba et al.,

2015

244 trichloromethane 0.425 0.49 0.15 0.02 0.6167 0.0000 0.0000 1.0 0.0 -4.46 -4.56 Baba et al.,

2015

245 triglycol nicotinate 0.950 1.58 0.37 1.78 1.9121 0.0000 0.0000 1.0 0.0 -8.08 -7.16 Zhang et al.,

2012

246 urea 0.501 1.49 0.83 0.84 0.4646 0.0000 0.0000 1.0 0.0 -7.93 -7.64 Zhang et al.,

2012

247 water 0.000 0.45 0.82 0.35 0.1673 0.0000 0.0000 1.0 0.0 -6.28 -6.43 Zhang et al.,

2012

a _K

p in units of cm/s; values of solute descriptors of neutral compounds taken from Abraham et al. (2009), Abraham et al. (2007), Abraham et al. (2008), Stephens et al.

(2012) and Zhang et al. (2012) or obtained as described before(Abraham et al., 2015a; Abraham et al., 2015b; Clarke and Mallon, 2012); ionic descriptors obtained as described before (Abraham and Acree, 2016). b _{Cited studies where log K}

23

We made a distinction between skin permeation through stratum corneum or through full

thickness skin or through intermediate thickness skin, by the use of indicator variables. For

permeation through the stratum corneum, the indicator variable is zero because this is our

‘standard system’. In column ‘Inter’, Table 2, all values are zero except for permeation through

intermediate thickness where the indicator value = 1. In column ‘Full’ all values are zero except

for permeation through full thickness skin where the indicator value = 1.

Regression of the values of log K

against the descriptors in Eq. 2 and the two indicator

variables ‘Inter’ and ‘Full’ leads to Eq. 4.

log K

= - 5.182(0.126) + 0.185(0.085) E - 0.617(0.057) S - 0.373(0.095) A - 2.412 (0.091) B

+ 1.763(0.081) V - 1.440(0.122) J

_{+ 2.461(0.113) J}

_{- 0.121(0.099) Inter}

- 0.299(0.139) Full

N = 247 SD = 0.430 R

= 0.869 F = 174.70 PRESS = 47.550 Q

= 0.858

PSD = 0.448

(4)

Here and elsewhere, N is the number of compounds or species studied, R

_{is the squared}

correlation coefficient, SD is the standard deviation, and F is the Fisher F-statistic. PRESS and

Q

are the leave-one-out statistics and PSD is the predicted standard deviation (Abraham et

al., 2009). The SD values for the coefficients are in parentheses. The coefficient 0.121 for the

indicator variable ’inter’ is very small, only just larger than the SD value, and exclusion of this

term results in Eq. 5.

log K

= - 5.311(0.071) + 0.159(0.082) E - 0.617(0.057) S - 0.352(0.094) A - 2.401(0.091) B +

1.782 (0.079) V - 1.448(0.123) J

_{+ 2.450(0.113) J}

_{- 0.190(0.108) Full}

24

If both of the terms in the indicator variables are left out, Eq. 6 is obtained.

log K

= - 5.328(0.071) + 0.137(0.082) E - 0.604(0.057) S - 0.338(0.094) A - 2.428(0.090) B +

1.797(0.079) V - 1.485(0.121) J

_{+ 2.471(0.113) J}

-N = 247 SD = 0.432 R

_{= 0.866 F = 221.48 PRESS = 47.335 Q}

_{= 0.858 PSD = 0.445}

(6)

From a comparison of Eqs. 4, 5 and 6, it can be seen that the inclusion of the ‘Inter’

variable makes no difference to the statistics of the LFER equation. The effect of the ‘Full’

indicator variable is very small, and we suggest that Eq. 6 be used in the prediction of further

values of log K

. What our analysis indicates is that differences in the thickness of skin used

make very little difference to the actual experimental value of K

.

Eq. 6 shows reasonably similar coefficients to our previous equation deduced from only

118 compounds, but with better values of SD (0.432) and R

_{(0.866). To prevent overfitting,}

the predicted R

(Q

) was calculated by the leave-one-out statistics, which may indicate how

well the model predicts new observations. Q

of Eq. 6 is 0.858, very close to the R

value of

0.866. This indicates that Eq. 6 can provide valid predictions for new observations without

overfitting. The predictive standard deviation (PSD) can also be obtained using the same

statistics; this gives the predictive accuracy of regression models (Abraham et al., 2009). The

PSD value of Eq. 6 is 0.445, which indicates that Eq. 6 is a good predicting model for log K

,

especially for the cases including ions and ionic species. In Figure 2, a plot of observed log K

versus predicted log K

is shown for all the compounds and species involved into the

25

In the construction of Eq. 6, we made an approximation of the ratio K

(n)/K

(i), which is

deduced from our previous model

(Zhang et al., 2012)

and the known descriptors, to estimate

the values of K

(n) and K

(i) of partially ionized compounds in Table 2. Now we use Eq. 6 to

calculate the values of K

(n)/K

(i), as shown in Table 3. Table 3 reveals that neutral acids and

bases permeate across the human skin very much faster than their ionic species, but the

actual ratio depends on their structures.

Table 3. Calculated values of Kp

(n)/K

(i) using Eq.6

Acids

K

(n)/K

(i)

Bases

K

(n)/K

(i)

C

H

COOH

35

4-MeC

H

CH

NHMe

40

C

H

(CH

)

COOH

45

4-MeC

H

CH

NHEt

43

C

H

(CH

)

COOH

45

4-MeC

H

CH

NHPr

44

C

H

(CH

)

COOH

52

4-MeC

H

CH

NHBu

43

C

H

(CH

)

COOH

38

4-MeC

H

CH

NH(CH

)

Me

41

chloroacetic acid

66

4-MeC

H

CH

NH(CH

)

Me

65

bromoacetic acid

108

4-MeC

H

CH

NH(CH

)

Me

58

dichloroacetic acid

45

alprenolol

266

dibromoacetic acid

22

propranolol

505

bromochloroacetic acid

22

sufentanil

352

trichloroacetic acid

21

lidocaine

75

piroxicam

13

meperidine

121

salicylic acid

24

fentanyl

900

naproxen

39

codeine

1323

indomethacin

137

ibuprofen

48

ketoprofen

52

flurbiprofen

57

diclofenac

51

ethacrynic acid

71

linolenic acid

229

26

our previous paper (Zhang et al., 2012), we used our constructed equation to predict values

of log K

for skin permeation for the sodium and tetraethylammonium ions, and we can do

the same through Eq. 6. Values are for Na

_{: -8.12 (obs) (Zhang et al., 2012), -7.41 (calc) (Zhang}

et al., 2012) and -7.55 (this work), and for Et

N

: -7.84 (obs) (Zhang et al., 2012), -6.48 (calc)

(Zhang et al., 2012)

and -6.38 (this work), so that it is possible to predict log K

for permanent

ions with no more than a set of simple descriptors (Abraham and Acree, 2016).

We illustrate the prediction of log K

with the examples shown in Table 4, for species that

have never been studied in terms of skin permeation. We can extend our predictions as

follows. In Eq. 3, values of the fraction ionized and neutral, F

and F

, depend on the pK

of the

solute and the pH of the donor solution. Eq. 3 can then be used in reverse, and a total value

of log K

can be calculated for any set of F

and F

values. Since these depend on the pH of the

donor solution, this amounts to a calculation of log K

as a function of pH. We illustrate this

in Figure 3 for ketoprofen, an acid with a pK

of 4.30; experimental data for the neutral and

ionized forms from Zhang et al. (2012).

Table 4. Prediction of log K

for some neutral and ionic species

Species E S A B V J+ J- log Kp (pred) 3,4-dimethoxybenzoic acid 0.95 1.65 0.57 0.75 1.3309 0.000 0.000 -5.82 3,4-dimethoxybenzoic acid, anion 1.04 3.93 0.00 3.17 1.3094 0.000 2.190 -7.49 bupivacaine 1.32 2.10 0.34 1.33 2.5139 0.000 0.000 -5.24 bupivacaine, cation 1.17 4.67 2.92 0.00 2.5354 1.592 0.000 -6.78

Eq. 3 and Figure 3 can be used to explain why models that do not distinguish between

neutral and ionic species, still yield reasonable statistical results. Because K

(n) is very much

larger than K

(i), partial ionization results in only a small diminution in the observed K

value.

Thus for ketoprofen, at pH = 4.3, when it is 50% neutral, our calculated log K

is -5.55 as

27

is only 30% in the neutral form, our calculated log K

is -5.76, only 0.50 log units less than for

the 100 % neutral species. Unless a particular compound is largely in the ionized form, use of

neutral descriptors and neglect of ionization will lead to calculated log K

values that are not

too far out-of-line.

We cannot compare the result shown in Figure 3 with any previous such results, because

this appears to be the first time that log K

values have been predicted as a function of pH in

this way. Indeed, we cannot compare our equation for permeation of neutral molecules and

ionic species, Eq. 6, with any previous equation that includes ionic species other than our own

equation

(Zhang et al., 2012). What we can say is that our statistics for Eq. 6 compare

favorably with those reported for equations that deal only with neutral species. One of the

most recent, and successful, models for skin permeation is that of Baba et al.

(2015) who used

an SVM-Gaussian method in which 2732 descriptors per compound were initially computed.

Reduction to 11 descriptors yielded an equation for 169 compounds with R

_{= 0.867 and a}

root mean square error, RMSE = 0.423 log units. This can be compared to Eq. 6 where we use

only 7 descriptors from the beginning, and for 247 species find that R

_{= 0.866 and RMSE =}

0.425 log units.

CONCLUSION

The LFER method provides a very useful tool to construct a predictive model for human skin

permeability of neutral molecules, ions and ionic species. In this study, an equation has been

constructed using the experimental log K

of a large and varied set of compounds and species.

The equation can be used to predict the values of log K

for neutral molecules, ions and ionic

28

quite accurately. An advantage of our method over previous methods is that it provides valid

predictions of log K

for partially ionized compounds, in terms of the fractions of neutral and

ionic species that exist at some given pH of the donor solution. We found that for ionizable

compounds at low degrees of ionization (that is, less than 50%), the experimental values of

log K

do not deviate markedly from that for the neutral molecules. By a critical analysis via

LEERs, it was confirmed that the thickness of skin exerts very little influence on the

experimental value of log K

.

ACKNOWLEDGEMENT

We are very grateful to Dr. Wei Huang (Software School, Xiamen University, China) and Dr Jia

He

of Environmental Sciences, Beijing 100012, China) for help with the statistical analysis.

.

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32

Legend to Figures

Figure 1. Distribution of log K

(cm/s) of the compounds and species in our data set.

Figure 2. A plot of observed log K

(cm/s) versus calculated log K

(cm/s) for all the

compounds and species involved in the calculation of Eq. 6. The solid line corresponds to ideal

agreement. Markers: ○, neutral molecules;

■

, cations from protonated bases; ♦, anions from

deprotonated acids.

Figure 3. A plot of values of log K

(cm/s) for ketoprofen as a function of the pH of the donor